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Last Modified: 2:01pm 10 Aug 11

The best place to put a TV satellite

Consider two satellites in orbit around the Earth: A is very close, B is far away.

The result is that satellite A travels a small distance with a high speed, but satellite B must cover a larger distance while moving at a lower speed. The periods of the two satellites must be very different.

For example, consider the International Space Station, which has an altitude of about 360 km.

  1. What is the distance between ISS and the center of the Earth?
  2. What is the acceleration of the ISS in its orbit? (Hint: use law of gravity)
  3. What is the velocity of the ISS in its orbit? (Hint: use centripetal acceleration formula)
  4. How long does it take ISS to complete one orbit around the Earth?
  5. Optional: Which way does ISS appear to move across the sky? If you can see it when it is just above above your local horizon, estimate how long it will take to cross the sky. (Hint: draw a big picture)

This means that if we stand on the ground and look up at night, we occasionally see the ISS fly across the sky.

If the ISS carried TV transmission equipment, our satellite TV dishes would have to track its motion across the sky; that's hard. Even worse, we wouldn't be able to see it most of the time. No TV?! Argh!

So, to prevent this catastrophe, kindly network executives have placed special satellites in orbits which have larger radii than that of ISS. That means that they move more slowly, AND they have to cover a larger distance. Their orbital periods are much longer .... exactly 24 hours. We call these "geosynchronous" satellites, because they always appear above the same spot on Earth. Another way to put it is that they always appear in the same spot in our sky. If you point a satellite dish at one today, it will still be looking at the right spot tomorrow -- and the next day -- and the next day -- and so on.

  1. What is the period of a geosynchronous satellite, in seconds?
  2. Write an equation which relates the period of a satellite's orbit to its orbital radius r and speed v
  3. Write another equation which describes the centripetal acceleration of a satellite (v-squared over r) in terms of capital G and the mass of the Earth
  4. Put those two equations together to solve for the special radius r of an orbit which has a period of exactly 24 hours
  5. Optional: What would the radius of a luna-synchronous satellite orbit be?
Sorry, we could not find this page | RIT CIS - Center for Imaging Science

Sorry, we could not find this page

We apologize, but the page you were looking for is not available. Most of our material is available from the menus above.

Last Modified: 2:01pm 10 Aug 11

Adapted from Prof. Michael Richmond.